Tight asymptotics of clique-chromatic numbers of dense random graphs

The clique chromatic number of a graph is the minimum number of colors required to assign to its vertex set so that no inclusion maximal clique is monochromatic. McDiarmid, Mitsche and Pra\l at proved that the clique chromatic number of the binomial random graph $G\left(n,\frac{1}{2}\right)$ is at most $\left(\frac{1}{2}+o(1)\right)\log_2n$ with high probability. Alon and Krivelevich showed that it is greater than $\frac{1}{2000}\log_2n$ with high probability and suggested that the right constant in front of the logarithm is $\frac{1}{2}.$ We prove their conjecture and, beyond that, obtain a tight concentration result: whp $\chi_c\left(G\left(n,1/2\right)\right) = \frac{1}{2}\log_2 n - \Theta\left(\ln\ln n\right).

Reconstruction of graph colourings

A $k$-deck of a (coloured) graph is a multiset of its induced $k$-vertex subgraphs. Given a graph $G$, when is it possible to reconstruct with high probability a uniformly random colouring of its vertices in $r$ colours from its $k$-deck? In this paper, we study this question for grids and random graphs. Reconstruction of random colourings of $d$-dimensional $n$-grids from the deck of their $k$-subgrids is one of the most studied colour reconstruction questions. The 1-dimensional case is motivated by the problem of reconstructing DNA sequences from their `shotgunned' stretches. It was comprehensively studied and the above reconstruction question was completely answered in the '90s. In this paper, we get a very precise answer for higher $d$. For every $d\geq 2$ and every $r\geq 2$, we present an almost linear algorithm that reconstructs with high probability a random $r$-colouring of vertices of a $d$-dimensional $n$-grid from the deck of all its $k$-subgrids for every $k\geq(d\log_r n)^{1/d}+1/d+\varepsilon$ and prove that the random $r$-colouring is not reconstructible with high probability if $k\leq (d\log_r n)^{1/d}-\varepsilon$. This answers the question of Narayanan and Yap (that was asked for $d\geq 3$) on "two-point concentration" of the minimum $k$ so that $k$-subgrids determine the entire colouring. Next, we prove that with high probability a uniformly random $r$-colouring of vertices of a uniformly random graph $G(n,1/2)$ is reconstructible from its full $k$-deck if $k\geq 2\log_2 n+8$ and is not reconstructible with high probability if $k\leq\sqrt{2\log_2 n}$. We further show that the colour reconstruction algorithm for random graphs can be modified and used for graph reconstruction: we prove that with high probability $G(n,1/2)$ is reconstructible from its full $k$-deck if $k\geq 2\log_2 n+11$ while it is not reconstructible with high probability if $k\leq 2\sqrt{\log_2 n}$

Safety of Spacecraft Participants Aboard Suborbital Reusable Launch Vehicles - Background Research

This presentation is an overview of commercial space safety regulatory environment and implications for government-sponsored spaceflight participants on commercial suborbital reusable launch vehicles

Safety of Spaceflight Participants Aboard Suborbital Reusable Launch Vehicles

The anticipated advent of the U.S. Government sponsoring human-tended research on commercial suborbital flights necessitates the establishment of safety review procedures for federal agencies to allow government-sponsored spaceflight participants (SFPs) aboard these vehicles. Safety practices for National Aeronautics & Space Administration (NASA) personnel aboard aircraft, orbital rockets and platforms, and a non- NASA vehicle, the Soyuz, are summarized. The valuable Recommended Practices for Human Space Flight Occupant Safety, published by the FAA Office of Commercial Space Transportation (FAA-AST) in 2014, are summarized. Medical recommendations for operationally critical flight crewmembers, published by the Aerospace Medical Association Commercial Spaceflight Working Group, are reviewed. FAA-AST approved SFP training available at three U.S. commercial companies is summarized. Activities of ASTM International Committee F47 on Commercial Spaceflight, formed in 2016, are reviewed. Finally, safety comparisons are made with another challenging environment, deep sea submersibles

Spectro-temporal shaping of seeded free-electron laser pulses

We demonstrate the ability to control and shape the spectro-temporal content of extreme-ultraviolet (XUV) pulses produced by a seeded free-electron laser (FEL). The control over the spectro-temporal properties of XUV light was achieved by precisely manipulating the linear frequency chirp of the seed laser. Our results agree with existing theory, which allows retrieving the temporal properties (amplitude and phase) of the FEL pulse from measurements of the spectra as a function of the FEL operating parameters. Furthermore, we show the first direct evidence of the full temporal coherence of FEL light and generate Fourier limited pulses by fine-tuning the FEL temporal phase. The possibility to tailor the spectro-temporal content of intense short-wavelength pulses represents the first step towards efficient nonlinear optics in the XUV to X-ray spectral region and will enable precise manipulation of core-electron excitations using the methods of coherent quantum control.Comment: 5 pages, 3 figure

Synchronization of coupled stochastic limit cycle oscillators

For a class of coupled limit cycle oscillators, we give a condition on a linear coupling operator that is necessary and sufficient for exponential stability of the synchronous solution. We show that with certain modifications our method of analysis applies to networks with partial, time-dependent, and nonlinear coupling schemes, as well as to ensembles of local systems with nonperiodic attractors. We also study robustness of synchrony to noise. To this end, we analytically estimate the degree of coherence of the network oscillations in the presence of noise. Our estimate of coherence highlights the main ingredients of stochastic stability of the synchronous regime. In particular, it quantifies the contribution of the network topology. The estimate of coherence for the randomly perturbed network can be used as means for analytic inference of degree of stability of the synchronous solution of the unperturbed deterministic network. Furthermore, we show that in large networks, the effects of noise on the dynamics of each oscillator can be effectively controlled by varying the strength of coupling, which provides a powerful mechanism of denoising. This suggests that the organization of oscillators in a coupled network may play an important role in maintaining robust oscillations in random environment. The analysis is complemented with the results of numerical simulations of a neuronal network. PACS: 05.45.Xt, 05.40.Ca Keywords: synchronization, coupled oscillators, denoising, robustness to noise, compartmental modelComment: major revisions; two new section

3D-Simulation of electromagnetic and temperature fields in the continuous induction heaters

The quasi-3-D model was developed for continuous induction heating of billets with arbitrary cross section. This computer model is intended for evaluation of electrical and thermal both stationary and non-stationary processes of stage and continuous working regime an induction heater with magnetic and non-magnetic loading with any of cross section shape. The combination of the most effective numerical methods for modeling induction heating process was used in this software: Finite Difference Method (FDM), Finite Element Method (FEM), Boundary Element Method (BEM), Integral Equation Method (IEM) and their combination